Stability analysis of black holes by the $S$-deformation method for coupled systems
General Relativity and Quantum Cosmology
2019-02-20 v3 High Energy Physics - Theory
Abstract
We propose a simple method to prove the linear mode stability of a black hole when the perturbed field equations take the form of a system of coupled Schr\"odinger equations. The linear mode stability of the spacetime is guaranteed by the existence of an appropriate -deformation. Such an -deformation is related to the Riccati transformation of a solution to the Schr\"odinger system with zero energy. We apply this formalism to some examples and numerically study their stability.
Keywords
Cite
@article{arxiv.1809.00795,
title = {Stability analysis of black holes by the $S$-deformation method for coupled systems},
author = {Masashi Kimura and Takahiro Tanaka},
journal= {arXiv preprint arXiv:1809.00795},
year = {2019}
}
Comments
26 pages, 9 figures, v2: minor revisions, v3: minor revisions, to appear in Classical and Quantum Gravity